Apparatus for multiplication and other arithmetical processes



(No Model.) 2 Sheets-Sheet 1.

A E. HALSBY.

APPARATUS EoR MULTIELICATION AND OTHER ARITEMETIGAL PROCESSES.

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2 Sheets-Sheet 2.

lla-hated June 22 PROCESSES.

E. HALSEY.

(No Model.)

APPARATUS FOR MULTIPLIGATION AND OTHER ARITHMETIGAL No. 344,18l

UNITED STATES PATENT OFFICE.

EDWARD IIALsEY, oF sAAT Jose, CALIFORNIA.

APPARATUS FOR MULTIPLICATION AND OTHER ARITHMETICAL PROCESSES.

SPECIFICATION forming part of Letters Patent No. 344,181, dated June 22,1886.

Serial No. 178,479. (No model.)

.To all whom it may concern:

Be it known that I, EDWARD HALsEY, a citizen of the United States,residing in San Jose, in the county of Santa Clara and State ofCalifornia, have invented certain new and useful Improvements inMachines for Multiplying and Performing Similar ArithmetiealCalculations; and I do hereby declare that the following is a full,clear, and exact description of the same and in what manner the machineis used and operated, reference being had by gures and letters to theaccompanying drawings.

My invention has for its object to produce a machine for performingarithmetical operations in multiplication, division, and interest; andit consists in a certain construction and combination of parts ashereinafter explained, for operation as set forth.

Referring to the said drawings, Figure 1 is a top view of the machinewith all the slides in position ready for use. Fig. 2 is a erosssection.Fig. 3 shows the position of the slides and their numbers in workingexamples given inthe following description by way of eX- ample. Fig. 4is a view in full lines of the portion shown in dotted lines at theright hand of Fig. 1.

A represents a board or tablet forming the base of the machine, and B atop plate which covers the face of the board, excepting the portion atone end, where certain indica-ting lines and figures are located. Theplate B, while being firmly secured in place, is set clear of the faceof the board, to leave a space or way for a number of slides, C C, andthis space is divided, by means of the pins d d, into separate waysacross the board, in each of which a slide is held and guided. Theseslides have easy movement in these guides back and forth from theleft-hand end of the board, and they are turned up at this end to formthe stop and finger-piece C for each slide. At this end also is an indexpoint or line, C, that is used for setting the slide to the required oneof the lines of the indicator E on the board in the operation of workingan example. The lines of this table E are spaced as shown, and arenumbered from 1 to 8, inclusive, beginning at the end nearer the inneredge of the plate E. These numbers are placed at the top and bottom.Each slide is likewise divided by transverse parallel lines into spacesof equal width, and when any number of slides are set to one of thelines of the table E the spaces on the slides will register and be indirect line over one another.

In the top plate, B, are rectangular openings b b, ten in number, eachof suitable width to uncover and expose eight of the spaces on theslides, and of such length that such portion is exposed on the wholenine of slides. rl`hese spaces are designated by numbers from 1 to 9,inclusive, the tenth and last opening not being numbered with them, asit is employed for calculating interest, and is not used in eonnectionwith the table of linesEand the other openings, except in working suchexamples. Operations in multiplication and division are performed onlywith the other nine spaces.

Each slide is designated by a number placed at the extreme left alongthe edge of the plate B, beginning with No. 1 for the lowest slide andending with No. 9 at the top one.

In the machine described the table E and the spaces appropriated to eachopening b,one arranged to perform operation in figures covering eightplaces or to the ten millions place,the extremeright-hand line intableEand the extreme right-hand space of each slide in each oftheopenings b being units, the next one tens, and so on to the eightplaces. The slides are numbered in these spacesin the following manner:The unit-spaces on the first or lowest slide seen at the extreme rightthroughout the whole number of nine spaces b, show the several productsobtained by multiplying the number of the slide by the numberdesignating the opening. Thus in opening lis seen the number l on thetirst slide, on opening2 the number 2, in opening-3 thenumber 3, and soon, being the products of the slide-number multiplied by theopeninghumber. In the same manner slide No; 2 is provided with thenumerals 2 4L 6 S 10 12 11 1U 18, exhibited in the openings b, from leftto right, slide 3 with the numerals 3 6 9 12 15 1S 2l 2i 27, and in thesame manner throughout the remaining six slides. rlhe position of theseslide-numerals is in a vertical column along the righthand edge of eachopening b, when the points C3 of all the slides are set to register withline lOO 833333; on slide 4, vthe figures 111111; onslide 5, the figures1388888, and the remaining slides carrying the following figuresrespectively: slide 6, the figures 1666666; slide 7, the figures1944444; slide 8, the figures 2222222; slide 9, the figures 2499999.These figures may, when l properly pointed, represent the interest forone day on the number of dollars represented by i the slide-number atone per cent. per year of three hundred and `sixty days. The spaceluncovered by the opening VbX is divided intotwo parts -by thread orwire fg, stretched perpendicularly across it, and which marksltheydivision between dollars and cents in the row Iof figures on each slidein the various-operations performed wfhere this space is employed.

The ope-ration of the machine 1in Vmulti plying figures will beunderstood by Aperforming the following example:

the sixth place or to hundreds of thousands,

and therst figure to be multiplied is 2, the i slide corresponding tothat number is drawn out to .the hundredthousands place, yor unti-l'fits poi-nts C3 register with .line-Got the table! E, the first lslide-is drawn Vo'utto the --fth place f or line 5, the next slide set to thefourth: place, the third slide to :the-third place, .the seventh slideto the second place, and the. fifth to the first orunits place on thetable' E. Then .from .the openings 3, 4, and .9 iin. succession aretakien the sums :that will beu obtained by adding up the-several-colunrnsfofil gures exposed, the num-bers of t-heopeningsy thustakenbeing those of the multipliergivem i and .resulting sums will be asfollows: from4 openingSthe sum 658125, which results from the additionof several figures:

j 76561875 Y gives the product required..

tion of Ytheigures seen -in the-openings b the sum that can be foundthenearest to the dividend, taken asy many figures thereof as thedivisor is found to be contained in it, and the number of the opening inwhich this sum is found will be the first figure for the quotient. Thissum being subtracted and a new dividend formed in the usual manner, theopenings b are again examined to obtain in one of them the sum nearestto that of the new dividend, and when found the number of the opening bshows the second figure of the quotient, and so on until the example isfinished.

The method of calculating interest by means ofthe machine is based onthe principle of lfinding the amount which in one day at one per cent.per year will produce the same amount of interest as a given sum at agiven rate for a given time will produce, and then .by setting theslides to the lines-ot' `the table E :according to the sum vascertainedthe given interest will =be the sum ofthe figures exposed to view in thelast openings bx.

those on the right are cents Aand decimal parts. l

The vfollowing example in simple interest y ,will .illustrate the kmodelof operation to Vfind N ow, as `the multiplicand contains tigures vto lthe interest on $625 at three per cent. for three months, twenty-sevendays. This will be equal to $18.75 at one per cent. for the .same time,or one hundred and'seventeen days;

or $18.75 117 will be the interest at one per cent. for one day von$219,375. Having set the yslides from v-6 Vto 1 inclusive to registerwiththe lines 2 1 9 3 7 5, respectively, on the table E, the following.figures 'will be rexposed .in the opening lb".

i fest on $625.00 for :the given time.

Having 'thus fully described my invention,

whatI claim, and desire vto secure by Letters i Patent. is-

1. The combination of thefra'me composed f fof -the board A and topplate, B, the former Y Y ihaving the f'tableof lines and numbers E, .andfrom the-opening 4 the sum 87.7 500, ifi-om the g opening 9the sufm1974375, which beingadded E las follows the latter provided with 'theopenings b b, each designated by number, and the numbered g slides C C,having their surfaces spaced :and marked with figures, which areobtained by multiplying lthe `nuxnberof the slide successively by theseveral `numerals designating the openings and placing the product insuch opening, substantially as described, for operas tion as set forth.

rBhe'operation-rot' division yis simply the freverse fof that Vrequiredin multiplying, ythe slides being set in the same manner with`reference-to the lines of the table E `to gi-vethe. figures of thedivision,'and then by examinaf 2. In a machine/ofthe characterdescribed,the numbered slides C C, having their faces divided vby spaced lines,Ainto ythe spaces `ot' which are placed numbers vthat are obtainedbyfmultiplying the designating number ofthe slide bythe numerals froml 1to l9,inclusive,in

The figures -shown to the left of Athe lineg are dollars, and

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succession for operation with reference to a theinterest at one percent.for one day on from plate, as B, having openings b, equal in numone tonine dollars, inclusive, and the table E ber to the numerals taken formultipliers, as at the opposite end, for operation as set forth.

set forth. In testimony that I claim the foregoing I 5 3. Thecombination 0f the plate B, having have hereunto set my hand and seal.

opening bx, with the line-wire g of the slide C C, numbered from l t0 9,inclusive, and I EDVARD HALSEY [L' s] adapted to be moved .back andforth beneath fitnessesz said opening, and having on the end portion C.W. M. SMITH, Io beneath said plate numbers which represent CHAs. E.KELLY.

